On the automorphism group of the p-adic group ring of a metacyclic p- group. II
type: Item
instance of: scholarly article
title: On the automorphism group of the p-adic group ring of a metacyclic p- group. II
zbMATH Open document ID: 0597.16010
DOI: 10.1016/0021-8693(86)90073-6
author: Katsusuke Sekiguchi
published in: Journal of Algebra
publication date: 1986-01-01T00:00:00Z
review text: In a recent paper [ibid. 82, 488-507 (1983; Zbl 0539.16006)] the author proved that for certain metacyclic p-groups G, \(Outcent(Z_ pG)=1\), where \(Z_ pG\) is the group ring of G over the ring of p-adic integers \(Z_ p\). Reference is made to the review of that paper for definitions. The purpose of the present paper is to extend the author's previous result to include all metacyclic p-groups, p an odd prime. Thus, the author proves: If G is a metacyclic p-group, p odd, then \(Outcent(Z_ pG)=1\). The author notes that it follows from this result that if G is any metacyclic p-group, p odd, then \(Outcent(Z_ qG)=1\) for any prime q.
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 16W20
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 16H05
Mathematics Subject Classification ID: 20B27
zbMATH DE Number: 3961872
zbMATH Keywords: central and inner automorphisms
zbMATH Keywords: orders
zbMATH Keywords: metacyclic p-groups
zbMATH Keywords: group ring
zbMATH Keywords: ring of p-adic integers
reviewed by: Joseph L. Zemmer
MaRDI profile type: Publication
full work available at URL: 0021-8693(86)90073-6
OpenAlex ID: W4206288288
cites work: Picard groups and automorphism groups of integral group rings of metacyclic groups
cites work: The Picard Group of Noncommutative Rings, in Particular of Orders
cites work: Class Groups and Picard Groups of Orders
cites work: Q3218257
cites work: On the automorphism group of the p-adic group ring of a metacyclic p- group
description: scientific article; zbMATH DE number 3961872